Mo et al. [1]} considered \( (p,1) \)  proportionally fair algorithm where \( p \)  is the vector of target queue size of the connections. Let \( ((Ad_Q)^i + d_{prop}^i), d_{prop}^i, w_i(t) \)  and \( x_i(t) \)  denote the total delay, propagation delay, current window size and data rate of user \( i \) , respectively. They update user's window size based on the following system of differential equations,
\(&& \frac{d w(t)}{dt} = -\alpha \frac{d_{prop}^i}{((Ad_Q)^i + d_{prop}^i)} \frac{s_i(t)}{w_i(t)}, \\&& s_i = w_i - x_i d_{prop}^i -p_i. \nonumber \) 
